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Communications in Mathematical Physics

, Volume 224, Issue 1, pp 133–152 | Cite as

Resonance Theory for Schrödinger Operators

  • O. Costin
  • A. Soffer
Article

Abstract:

Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. The exponential decay rate of resonances is addressed; its uniqueness in the time dependent picture is shown in certain cases. The relation to the existence of meromorphic continuation of the properly weighted Green–s function to time dependent resonance is further elucidated, by giving an equivalent time dependent asymptotic expansion of the solutions of the Schrödinger equation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • O. Costin
    • 1
  • A. Soffer
    • 1
  1. 1.Department of Mathematics, Rutgers UniversityPiscatawayUSA

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